| Gender | promote | nopromote |
|---|---|---|
| Male | 21 | 3 |
| Female | 14 | 10 |
\[ P(promote\,|\,M) = 21/24 = 0.875 \\ P(promote\,|\,F) = 14/24 = 0.583 \]
At a first glance, does there appear to be a relatonship between promotion and gender?
We saw a difference of almost 30% (29.2% to be exact) between the proportion of male and female files that are promoted. Based on this information, which of the below is true?
\(H_0\), Null Hypothesis: "There is nothing going on".
\(H_A\), Alternative Hypothesis: There is something going on.”
H0 : Defendant is innocent vs. HA : Defendant is guilty

The hypothesis test gives us:
\[ P(\textrm{data}\,|\,\textrm{H}_0) \]
It doesn't give us:
\[ P(\textrm{H}_0\,|\,\textrm{data}) \]
What is the null hypothesis?
What is the alternative hypothesis?
What is our test statistic?
| Gender | promote | nopromote |
|---|---|---|
| Male | 21 | 3 |
| Female | 14 | 10 |
We can compute our observed test statistic:
\[ d_{obs} = \hat{p}_{M} - \hat{p}_{F} \\ d_{obs} = 21/24 - 14/24 = .29 \]
Face cards: promoted
Number cards: not promoted
\[ d = \hat{p}_{M} - \hat{p}_{F} \]
Repeat steps 1-3 and store each one.
Do the results of the simulation you just ran provide convincing evidence of gender discrimination against women, i.e. dependence between gender and promotion decisions?